if G is a group of order 2n then show that it has an element of order 2 ( and odd number of them)(adsbygoogle = window.adsbygoogle || []).push({});

i've been thinking about this...and i think i've gotten somewhere...

e belongs to G and o(e) = 1

now if there's no element of order 2 in G...we're looking at elements which are not their own inverses...such elements come in pairs, so i guess there lies the contradiction...

i don't have a clue as to how to show that there are odd number of elements of order two.

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